Convert a curve to a mesh with a user defined resolution
Bezier Curves

The curve resolution is already an exact parameter that drives the resolution of the surface (for example in U direction), but it is taking into account the number of faces, not vertices.

For a curve without V resolution (0), the faces collapse into edges, so you'll have a starting vertex, than an edge(1) followed by a vertex (1), than an edge(2) followed by a vertex (2), ... than an edge(n) followed by a vertex (n).

At the end the number of vertices is always n+1, with n as the number of edges/faces resulting from the moltiplication of the resolution and the number of segments of your spline. 

The following example consider a spline made of 1 segment (2 control points). See how in this case the resolution is equal to the number of resulting edges.



The final formula should be:


  n° of final vertices = n° spline segments * resolution + 1


Nurbs Curves

Nurbs have a different mathematical implementation from Beziers.

They require at least 3 control points to build a proper geometry. If you set the Resolution parameter to 1, you can see how the number of edges constituting the figure is equal to the number of control edges minus 1. But as the number of final vertices is equal to the number of final edges plus one (as seen before), we can say that the numberof final vertices is equal to the number of control edges that the Nurbs has.

So for example a Nurbs curve made with 5 control edges, will result in a curve with 5 vertices once converted to mesh, if the resolution is set to 1.

As the tooltip says, the Resolution Parameter controls the number of subdivision per segment. Here's a few result for the previous example:


Res: 1 -> 5 vertex (4 edges)
Res: 2 -> 5*2 = 10 vertex (9 edges)
Res: 3 -> 5*3 = 15 vertex (14 edges)
Res: 4 -> 5*4 = 20 vertex (19 edges)
....
Res: n -> 5*n vertex (5*n-1 edges)


The final formula should be:


  n° of final vertices = n° of control edges * resolution